find the gradients of line a and b

Given:

Total number of gym members = 685

257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.

To find:

a. The venn diagram.

b. The probability that a member uses the treadmill only?

Solution:

(a)

We have,

Total number of gym members = 685

Treadmill user = 257

Elliptical user = 157

Who use both = 85

Only treadmill user is:

[tex]257-85=172[/tex]

Only Elliptical used

[tex]157-85=72[/tex]

Therefore, the venn diagram for the given situation is shown below.

(b)

The member who use treadmill only = 172

Total user = 685

The probability that a member uses the treadmill only is:

[tex]P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}[/tex]

[tex]P(\text{Only treadmill})=\dfrac{172}{685}[/tex]

Therefore, the probability that a member uses the treadmill only is [tex]\dfrac{172}{685}[/tex].

Answer:

x = 10.7

Step-by-step explanation:

We have:

[tex]\frac{x}{sin 90}[/tex] = [tex]\frac{9.2}{sin59}[/tex]

=> x × sin59 = 9.2 × sin90

=> x × sin59 = 9.2

=> x = 9.2 ÷ sin59

=> x = 10.733027...

=> x = 10.7 (Round to the nearest tenth)

<3 Have a nice day!!

Answer:

a. 18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                      [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^2_0 {x(4x^2 + 1)} \, dx[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

Step-by-step explanation:

Given

See attachment for circle

Required

The circle equation

First, we get the radius of the circle.

From the attachment, we have:

[tex]r = 3[/tex]

Next, the center of the circle

[tex](h,k) = (-1,1)[/tex]

The equation of the circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

This gives:

[tex](x - -1)^2 + (y - 1)^2 = 3^2[/tex]

[tex](x +1)^2 + (y - 1)^2 = 3^2[/tex]

Expand

[tex]x^2 + 2x + 1 + y^2 - 2y + 1 = 9[/tex]

Collect like terms

[tex]x^2 + y^2 + 2x - 2y + 1 + 1 - 9 = 0[/tex]

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

Hence, the equation in general form is:

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

Hi!

These two angles are alternate interior angles, so they are congruent. Thus:

∠A = ∠B

6x + 5 = 4x + 45

Solve for x:

2x + 5 = 45

2x = 40

x = 20

Solve for ∠A by substituting in this value:

∠A = 6(20) + 5 = 125°

Answer:

c) x=126

Step-by-step explanation:

tell me if I get it right

Answer:

5418.54 ft

Step-by-step explanation:

So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.

-19. 26+ 5437.8= 5418.54

Now just add on the units!

Hope this helps!

Answer:

Answer:

5418.54 ft

Step-by-step explanation:

Answer:

5418.54 ft

Step-by-step explanation:

So sea level is 0, okay? So Nadia (her name is more than 3 letters and I'm lazy so from now on she'll be reffered to as "N") is at -19. 26 ft. N goes up 5,437.8 ft, so we add this value on.

-19. 26+ 5437.8= 5418.54

Answer:

[tex]V=34.64\ cm^3[/tex]

Step-by-step explanation:

Given that,

The side of an equilateral prism = 4 cm

The altitude of the prism = 5 cm

We need to find the volume of the prism. The formula for the volume of a prism is as follows :

[tex]V=A\times h[/tex]

Where

A is the area of equilateral triangle, [tex]A=\dfrac{\sqrt3}{4}a^2[/tex]

So,

[tex]V=\dfrac{\sqrt3}{4}a^2\times h\\\\V=\dfrac{\sqrt3}{4}\times 4^2\times 5\\\\V=34.64\ cm^3[/tex]

So, the volume of the prism is equal to [tex]34.64\ cm^3[/tex].

Answer:

4 pounds

Step-by-step explanation:

take 20% off the original price. 20(0.20)= 4

So that's a discount of 4 pounds and the sale price is 16 pounds.

The savings is 4 pounds on 1 shirt.

Answer:

From left to right, fill in 3.5 and 6.5

Step-by-step explanation:

Use the given formula to calculate y for the given values of x.

When x = 0.5, y = 3(0.5) + 1/0.5

y = 1.5 + 2

y = 3.5 if x = 0.5

When x = 2, y = 3(2) + 1/2

y = 6 + 0.5

y = 6.5 if x = 2

Answer:

90

Step-by-step explanation:

Answer:

A. It acts perpendicular to an object

Given:

Axis of symmetry of a parabola is [tex]x=4[/tex].

A point on the parabola is (0,2).

To find:

The another point on the parabola.

Solution:

The point (0,2) lies on the parabola and the axis of symmetry of a parabola is [tex]x=4[/tex].

It means, the another point on the parabola is the mirror image of (0,2) across the line [tex]x=4[/tex] because the parabola is symmetric about the axis of symmetry.

If the point is reflected across the line [tex]x=4[/tex], then

[tex](x,y)\to (-(x-4)+4,y)[/tex]

[tex](x,y)\to (-x+4+4,y)[/tex]

[tex](x,y)\to (-x+8,y)[/tex]

Using this rule, we get

[tex](0,2)\to (-0+8,2)[/tex]

[tex](0,2)\to (8,2)[/tex]

Therefore, the other point on the parabola is (8,2).

Answer:

t > 28

Step-by-step explanation:

Answer:

10-5=5 answer is 8^5

Step-by-step explanation:

Answer:

[tex]8^{5}[/tex]

Step-by-step explanation:

[tex]\frac{8^{10} }{8^{5} }[/tex]

Where are there more 8's ?

top

How many more?

5

Then they stay on top of fraction.

Another way :

[tex]x^{a}[/tex] ÷ [tex]x^{b}[/tex] = [tex]x^{a-b}[/tex]

[tex]8^{10}[/tex]  ÷ [tex]8^{5}[/tex] = [tex]8^{10-5}[/tex] = [tex]8^{5}[/tex]

Hello!

8y + 3 > 15y + 52 <=>

<=> 8y - 15y > 52 - 3 <=>

<=> -7y > 52 - 3 <=>

<=> -7y > 49 <=>

<=> y < -7 => y ∈ { -∞; -7 }

Good luck! :)

Answer:

A. 4x² + 9x/4 - 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x/4 - 3

g(x) = 4x² + 2x - 4

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

(1.6, 6)

Step-by-step explanation:

[tex] ln({e}^{5 - 2x} = 6)[/tex]

[tex]5 - 2x = ln(6) [/tex]

[tex]2x = 5 - ln(6) [/tex]

[tex]x = \frac{5 - ln(6) }{2} [/tex]

y = 6

Answer:

0.054, 0.405, 0.45, 0.54

Answer:

0.054, 0.405, 0.45, 0.54

Step-by-step explanation:

1. The 0 after the decimal point makes it the smallest

2. 405/1000 < 45/100

3. 45/100 < 54/100

Answfirst one

Step-by-step explanation:

hope it helps thank u

Answer:

first one

Step-by-step explanation:

2 students have the same age but different heights.

since age is the input and height is the output. in order to be a function one must have exact one output for one input.

since the heights of students in Tessa 's class are not a function of their ages (one input must have two outputs) two students of same age must have different heights.

Step-by-step explanation:

We can start by writing an equation to describe the data set. For 2D data, one equation form we can use is y=m*x + b, where x is the input and y is the output. Since yuan are put in and dollars are put out, x represents yuan and y represents dollars in this instance.

To find the equation, we can start by plugging in two points, such as (50, 1.25) and (100, 7.5). The slope, or m, is equal to the change in y/change in x, or

(7.5-1.25)/(100-50) = 6.25/50

= 0.125. This means that for each yuan put in, 0.125 dollars come out, according to the formula.

Next, we must find b. Plugging 0.125 in for m and taking a set of points, such as (50, 1.25), we get

1.25 = 50(0.125) + b

1.25 = 6.25 + b

subtract both sides by 6.25 to isolate the b

-5 = b

Therefore, we can write our equation as

y = 0.125 * x - 5

In this equation, there is an exchange rate of 0.125, meaning that for each yuan put in, 0.125 dollars are coming out. The -5 symbolizes that for each transaction, 5 yuan are being lost, which is the fee for exchanging money.

To check if the equation works, we can try it for options such as (200, 20) and (250, 26.25). This does work, so we can move forward with our equation.

For (c), our equation is y = 0.125 * x - 5, with the y representing dollars, x representing yuan, 0.125 representing the exchange rate, and -5 representing the fee for exchaning mone

For (b), because 5 yuan are subtracted from the exchange rate for each transaction, it is fair to assume that there is a fee for exchanging money. There is a fee of 5 yuan per transaction. In dollars, using the exchange rate of 0.125 dollars per yuan, this is equal to 0.625 dollars

For  (a), the exchange rate is 0.125 dollars per yuan. We know this because for each yuan put in, 0.125 dollars are coming out after taking into account the fee

Step-by-step explanation:

the sum of angels of a triangle is 180°

130+ ? + (180-160) = 180

130+ ? +20= 180

150+ ? = 180

? = 30°

the missing angle is 30°

Answer:

Step-by-step explanation:

The area is:

We can find the area,

→ 2(3.5 × 2)+ (7 × 2) + 2(1.8 × 2)

→ 14 + 14 + 7.2

→ 35.2 cm²

Thus, the area is 35.2 cm².

Answer:

Let's define the high temperature as T.

We know that:

"four times T, was more than 2*T plus 66°C"

(i assume that the temperature is in °C)

We can write this inequality as:

4*T > 2*T + 66°C

Now we just need to solve this for T.

subtracting 2*T in both sides, we get:

4*T - 2*T > 2*T + 66°C - 2*T

2*T > 66°C

Now we can divide both sides by 2:

2*T/2 > 66°C/2

T > 33°C

So T was larger than 33°C

Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.

Then the range of possible temperatures is:

(33°C, ...)

Where we do not have an upper limit, so we could write this as:

(33°C, ∞°C)

(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)

Answer:1. = 4x+8  

2. 2a²-a+1

Step-by-step explanation:

1. ((x+2)+3x+6.  2. 2a(a-1)-a+1​

((x+2)+3x+6

= x+2+3x+6

= 4x+8

2a(a-1)-a+1

2a²-2a-a+1

2a²-a+1

Answer:

The first one and last one

Step-by-step explanation:

Answer:

1,2,5

Step-by-step explanation:

got it right on edge

Answer:

Step-by-step explanation:

I am sort. I have no idea

Answer:

The three straight paths intersect at different angles. In other words, the amountrequired to turn one path onto the other is different about each vertex. Thelargest angle is opposite the longest side, and the smallest angle is opposite theshortest side. If all three points of intersection look the same, the result is atriangle with three equal angles and three equal sides.

Step-by-step explanation:

Answer:

a³-9a

a³-9a

=a(a+3)(a-3)

Answer:

a = 1000, p = 10

Step-by-step explanation:

Given

y = - 3lg x + lg a

in the form y = mx + c ( m is the slope and c the y- intercept )

From the graph

(a)

c = 3 , then

lg a = 3 , that is

a = 10³ = 1000

(b)

Replace x by p and y = 0 in the equation

0 = - 3lg p + 3 ( subtract 3 from both sides )

- 3 = - 3lg p ( divide both sides by - 3 )

1 = lg p

p = 10 [ [tex]log_{10}[/tex] 10 = 1 ]